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Algorithms

Concrete quantum algorithm examples built with Qamomile.

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In this section: algorithm chemistry encoding error-correction machine-learning optimization primitive sample-based simulation variational

In other sections: integration resource-estimation tutorial usage

Hamiltonian Simulation with Suzuki–Trotter (Rabi oscillation)

Trotter–Suzuki product formulas on the Rabi model with empirical convergence orders.

Hybrid Quantum Neural Network (HQNN)

End-to-end CNN + quantum variational circuit on Fashion-MNIST with the parameter shift rule.

Möttönen Amplitude Encoding

Prepare an arbitrary real or complex amplitude vector via Gray-code Ry/Rz multiplexers, with three input modes (concrete, bound Vector[Float], runtime-parametric angles).

Multidimensional Quantum Fourier Transform

Implement multidimensional QFT and classical preprocessing for inputs whose grid sizes are not powers of two.

Pauli Correlation Encoding (PCE)

Solve a 20-variable MaxCut on just 3 qubits with Pauli Correlation Encoding, training a hardware-efficient ansatz against a tanh-relaxed surrogate and decoding via sign rounding.

QAOA for Graph Partitioning

End-to-end optimization example using OMMX, JijModeling, and QAOAConverter.

QAOA for MaxCut: Building the Circuit from Scratch

Build a QAOA circuit from scratch to solve MaxCut, then compare with the built-in qaoa_state.

Quantum-enhanced Markov chain Monte Carlo

Implement Quantum-enhanced MCMC using Trotter-decomposed time evolution.

Quantum Selected Configuration Interaction (QSCI)

Sample bitstrings from a quantum state, build an effective Hamiltonian, and diagonalize it classically with a strict variational guarantee.

Introduction to Quantum Error Correction

3-qubit bit-flip/phase-flip codes, Shor's 9-qubit code, and stabilizers.

Quantum Kernel Classification

Use quantum feature maps and kernel methods for classification on the make_circles dataset.

Stabilizer Formalism and the Steane Code

CSS construction, syndrome decoding, and transversal Hadamard.

Variational Quantum Eigensolver (VQE) for the Hydrogen Molecule

Build a molecular Hamiltonian with OpenFermion and find the ground state energy via VQE.